Between semi-closed sets and semi-pre-closed set

Abstract

In this paper a new class of sets, namely $\psi-\mathbf{closed\: set}$ is introduced for topological spaces. This class falls strictly in between the class of semi-closed sets and the class of semipreclosed sets. This class also sits strictly in between the class of semi-closed sets and the class of semi-generalized closed sets. We also introduce and study a new class of spaces, namely $\mathbf{semi-}\textrm{T}_{1/3}\:\mathbf{spaces}$. Further we introduce and study $\psi-\mathbf{continuous}$ maps and $\psi-\mathbf{irresolute}$ maps.